111=(2x+29)(2x+5)

Solution for 111=(2x+29)(2x+5) equation:

Simplifying
111 = (2x + 29)(2x + 5)

Reorder the terms:
111 = (29 + 2x)(2x + 5)

Reorder the terms:
111 = (29 + 2x)(5 + 2x)

Multiply (29 + 2x) * (5 + 2x)
111 = (29(5 + 2x) + 2x * (5 + 2x))
111 = ((5 * 29 + 2x * 29) + 2x * (5 + 2x))
111 = ((145 + 58x) + 2x * (5 + 2x))
111 = (145 + 58x + (5 * 2x + 2x * 2x))
111 = (145 + 58x + (10x + 4x2))

Combine like terms: 58x + 10x = 68x
111 = (145 + 68x + 4x2)

Solving
111 = 145 + 68x + 4x2

Solving for variable 'x'.

Combine like terms: 111 + -145 = -34
-34 + -68x + -4x2 = 145 + 68x + 4x2 + -145 + -68x + -4x2

Reorder the terms:
-34 + -68x + -4x2 = 145 + -145 + 68x + -68x + 4x2 + -4x2

Combine like terms: 145 + -145 = 0
-34 + -68x + -4x2 = 0 + 68x + -68x + 4x2 + -4x2
-34 + -68x + -4x2 = 68x + -68x + 4x2 + -4x2

Combine like terms: 68x + -68x = 0
-34 + -68x + -4x2 = 0 + 4x2 + -4x2
-34 + -68x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-34 + -68x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(17 + 34x + 2x2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(17 + 34x + 2x2)' equal to zero and attempt to solve:

Simplifying
17 + 34x + 2x2 = 0

Solving
17 + 34x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
8.5 + 17x + x2 = 0

Move the constant term to the right:

Add '-8.5' to each side of the equation.
8.5 + 17x + -8.5 + x2 = 0 + -8.5

Reorder the terms:
8.5 + -8.5 + 17x + x2 = 0 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + 17x + x2 = 0 + -8.5
17x + x2 = 0 + -8.5

Combine like terms: 0 + -8.5 = -8.5
17x + x2 = -8.5

The x term is 17x.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17x + 72.25 + x2 = -8.5 + 72.25

Reorder the terms:
72.25 + 17x + x2 = -8.5 + 72.25

Combine like terms: -8.5 + 72.25 = 63.75
72.25 + 17x + x2 = 63.75

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 63.75

Calculate the square root of the right side: 7.984359711

Break this problem into two subproblems by setting 
(x + 8.5) equal to 7.984359711 and -7.984359711.

Subproblem 1
x + 8.5 = 7.984359711

Simplifying
x + 8.5 = 7.984359711

Reorder the terms:
8.5 + x = 7.984359711

Solving
8.5 + x = 7.984359711

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = 7.984359711 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = 7.984359711 + -8.5
x = 7.984359711 + -8.5

Combine like terms: 7.984359711 + -8.5 = -0.515640289
x = -0.515640289

Simplifying
x = -0.515640289

Subproblem 2
x + 8.5 = -7.984359711

Simplifying
x + 8.5 = -7.984359711

Reorder the terms:
8.5 + x = -7.984359711

Solving
8.5 + x = -7.984359711

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = -7.984359711 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = -7.984359711 + -8.5
x = -7.984359711 + -8.5

Combine like terms: -7.984359711 + -8.5 = -16.484359711
x = -16.484359711

Simplifying
x = -16.484359711

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.515640289, -16.484359711}
Solution
x = {-0.515640289, -16.484359711}